Table of Contents

Cover

Title Page

Preface

Acknowledgments

Chapter 1: Introduction

1.1 General
1.2 Track Components
1.3 Characteristics of Railway Track Data
1.4 Railway Track Engineering Problems
1.5 Wheel–Rail Interface Data
1.6 Geometry Data
1.7 Track Geometry Degradation Models
1.8 Rail Defect Data
1.9 Inspection and Detection Systems
1.10 Rail Grinding
1.11 Traditional Data Analysis Techniques
1.12 Remarks
References

Chapter 2: Data Analysis – Basic Overview

2.1 Introduction
2.2 Exploratory Data Analysis (EDA)
2.3 Symbolic Data Analysis
2.4 Imputation
2.5 Bayesian Methods and Big Data Analysis
2.6 Remarks
References

Chapter 3: Machine Learning: A Basic Overview

3.1 Introduction
3.2 Supervised Learning
3.3 Unsupervised Learning
3.4 Semi-Supervised Learning
3.5 Reinforcement Learning
3.6 Data Integration
3.7 Data Science Ontology
3.8 Imbalanced Classification
3.9 Model Validation
3.10 Ensemble Methods
3.11 Big $c03-math-166$ and Small $c03-math-167$ ( $c03-math-168$ )
3.12 Deep Learning
3.13 Data Stream Processing
3.14 Remarks
References

Chapter 4: Basic Foundations of Big Data

4.1 Introduction
4.2 Query
4.3 Taxonomy of Big Data Analytics in Railway Track Engineering
4.4 Data Engineering
4.5 Remarks
References

Chapter 5: Hilbert–Huang Transform, Profile, Signal, and Image Analysis

5.1 Hilbert–Huang Transform
5.2 Axle Box Acceleration
5.3 Analysis
5.4 Remarks
References

Chapter 6: Tensors – Big Data in Multidimensional Settings

6.1 Introduction
6.2 Notations and Definitions
6.3 Tensor Decomposition Models
6.4 Application
6.5 Remarks
References

Chapter 7: Copula Models

7.1 Introduction
7.2 Pair Copula: Vines
7.3 Computational Example
7.4 Remarks
References

Chapter 8: Topological Data Analysis

8.1 Introduction
8.2 Basic Ideas
8.3 A Simple Railway Track Engineering Application
8.4 Remarks
References

Chapter 9: Bayesian Analysis

9.1 Introduction
9.2 Markov Chain Monte Carlo (MCMC)
9.3 Approximate Bayesian Computation
9.4 Markov Chain Monte Carlo Application
9.5 ABC Application
9.6 Remarks
References

Chapter 10: Basic Bayesian Nonparametrics

10.1 General
10.2 Dirichlet Family
10.3 Dirichlet Process
10.4 Finite Mixture Modeling
10.5 Bayesian Nonparametric Railway Track
10.6 Remarks
References

Chapter 11: Basic Metaheuristics

11.1 Introduction
11.2 Remarks
References

Chapter 12: Differential Privacy

12.1 General
12.2 Differential Privacy
12.3 Remarks
References

Index

End User License Agreement

List of Illustrations

Chapter 1: Introduction

Figure 1.1 Track structure components
Figure 1.2 Classification of random data
Figure 1.3 Classification of deterministic data
Figure 1.4 Engineering signals
Figure 1.5 Wheel–rail contact impacts
Figure 1.6 Wheel–rail interface
Figure 1.7 Regions of wheel/rail contact
Figure 1.8 Different types of switches and crossings
Figure 1.9 Schematized standard turnout and its components
Figure 1.10 Classification of track geometry models based on parameters' uncertainty
Figure 1.11 Linear representation of track geometry degradation and restoration based on the standard deviation of roughness
Figure 1.12 Nonlinear representation of track geometry degradation and restoration based on the standard deviation of roughness
Figure 1.13 Rail defects distribution
Figure 1.14 Cross-section of a rail
Figure 1.15 Transverse, vertical, and horizontal places of track
Figure 1.16 Surface regions of rail head
Figure 1.17 Repository of rail head surface classes: normal or noncritical surface
Figure 1.18 Rail defects per mile
Figure 1.19 Rolling contact fatigue. Courtesy: Johannes Bremsteller
Figure 1.20 Different rail maintenance strategies. Courtesy: Johannes Bremsteller

Chapter 2: Data Analysis – Basic Overview

Figure 2.1 Box plot for some track geometry parameters
Figure 2.2 Histogram for some track geometry parameters
Figure 2.3 Q–Q plot for some track geometry parameters
Figure 2.4 Time series data table – track surface inspection
Figure 2.5 Illustration of multivariate scatter plots for different inspection times

Chapter 3: Machine Learning: A Basic Overview

Figure 3.1 Overview of different classifier categories (Camps-Valls and Bruzzone (2009). Reproduced with the permission of John Wiley and Sons)
Figure 3.2 Illustration of data science ontology
Figure 3.3 Transformation of original data to feature space
Figure 3.4 Two hyperplanes (Fu et al. (2014). Reproduced with the permission of Springer)
Figure 3.5 Training and testing approach
Figure 3.6 Training, testing, and validation
Figure 3.7 Receiver operating characteristic (ROC) curve
Figure 3.8 Illustration of bagging procedure
Figure 3.9 Big $c03-math-172$ and small $c03-math-173$
Figure 3.10 Bias/variance decomposition
Figure 3.11 Bias/variance – method selection
Figure 3.12 A graphical representation of a regional split applied to a univariate scatterplot (Sekulic and Kowalski (1992). Reproduced with the permission of John Wiley and Sons)
Figure 3.13 (a) Examples for surface defects and (b) non-defective samples (Soukup and Huber-Mörk, 2014). Reproduced with the permission of Springer
Figure 3.14 CNN architecture for surface defect detection: two convolutional and pooling layers and a final fully connected layer (Soukup and Huber-Mörk, 2014). Reproduced with the permission of Springer
Figure 3.15 RBM structure
Figure 3.16 Generic DBN
Figure 3.17 DBN layer-wise training process. “ $c03-math-240$ ” is the input vector, while “ $c03-math-241$ ” are DBN hidden layers. In each training iteration, one DBN layer is considered as a hidden RBM layer. DBN arrows indicate the direction of the generative model
Figure 3.18 Deep learning CNN model architecture
Figure 3.19 Representation of clustering (Galvan-Nunez and Attoh-Okine, 2016). Reproduced with the permission of American Society of Civil Engineers
Figure 3.20 Clustering process (Galvan-Nunez and Attoh-Okine, 2016). Reproduced with the permission of American Society of Civil Engineers
Figure 3.21 Example of a hash table (El-Metwally et al., 2014). Repoduced with the permission of Springer
Figure 3.22 Example of a Bloom filter (El-Metwally et al., 2014). Repoduced with the permission of Springer
Figure 3.23 Count–min sketch idea
Figure 3.24 IWS sample signal
Figure 3.25 IWS application

Chapter 4: Basic Foundations of Big Data

Figure 4.1 The big data analysis pipeline (Jagadish, 2015). Reproduced with the permission of Elsevier
Figure 4.2 Railway big data
Figure 4.3 Big data environment
Figure 4.4 Landscape
Figure 4.5 Taxonomy of data model
Figure 4.6 Big data versus traditional data
Figure 4.7 Big data taxonomy
Figure 4.8 Five Vs of big data
Figure 4.9 Data size (Adarkwa, 2015). Reproduced with the permission of University of Delaware
Figure 4.10 MapReduce architecture (Attoh-Okine, 2016). Reproduced with the permission of Cambridge University Press
Figure 4.11 Pseudocode of the $c04-math-006$ -means algorithm
Figure 4.12 Pseudocode MapReduce-based $c04-math-008$ -means algorithm
Figure 4.13 Apache Spark

Chapter 5: Hilbert–Huang Transform, Profile, Signal, and Image Analysis

Figure 5.1 Illustration of the HHT
Figure 5.2 Sifting process
Figure 5.3 Part of synthetic data
Figure 5.4 Signal and IMF components
Figure 5.5 Plot of instantaneous wave number against distance for highest wave number component IMFs
Figure 5.6 Wavelet transform of synthetic data
Figure 5.7 Analysis of cross-level
Figure 5.8 Comparative analysis of cross-level at different months (June and July)
Figure 5.9 Analysis of surface (right)
Figure 5.10 Comparative analysis of surface (right)
Figure 5.11 Analysis of alignment (right)
Figure 5.12 Comparative analysis of alignment (right)
Figure 5.13 Post-processing ensemble empirical mode decomposition. Courtesy: Ding and Lin, 2010
Figure 5.14 Using BEMD to remove shadows
Figure 5.15 Subtraction of images
Figure 5.16 Preprocessing of track images
Figure 5.17 Preprocessing of track images
Figure 5.18 Schematic view of the axle box acceleration measuring and diagnosis system (Oregui et al., 2016). Reproduced with the permission of John Wiley and Sons

Chapter 6: Tensors – Big Data in Multidimensional Settings

Figure 6.1 3D tensor fibers
Figure 6.2 3D tensor slices
Figure 6.3 Cross-level measurement at different dates
Figure 6.4 Track geometry parameters measurements
Figure 6.5 Data structure for the cross-level
Figure 6.6 Loading plot for cross-level
Figure 6.7 Correlation analysis (matrix)
Figure 6.8 Loading plot for distance points
Figure 6.9 Data structure for cross-level, surface (right) and alignment on same date
Figure 6.10 Correlation matrix
Figure 6.11 Loading plots
Figure 6.12 Loading plots for points

Chapter 7: Copula Models

Figure 7.1 Pairs plot of the track geometry data set with scatterplots above and contour plots with standard normal margins below the diagonal
Figure 7.2 (a) $c07-math-278$ -Plot. (b) Chi-plot. (c) Empirical lambda function (black line), theoretical lambda function of a Student's $c07-math-279$ copula (gray line), as well as independence and comonotonicity limits (dashed lines)
Figure 7.3 Four-dimensional $c07-math-352$ -vine, where $c07-math-353$ Student's $c07-math-354$ copula, $c07-math-355$ Frank copula, $c07-math-356$ Normal/Gaussian copula, and $c07-math-357$ independent copula with corresponding empirical $c07-math-358$ values shown on the links with the copula family
Figure 7.4 Four-dimensional $c07-math-359$ -vine, where $c07-math-360$ Normal/Gaussian copula, $c07-math-361$ Student's $c07-math-362$ copula, $c07-math-363$ Frank copula, and $c07-math-364$ independent copula with corresponding empirical tau values shown on the links with the copula family

Chapter 8: Topological Data Analysis

Figure 8.1 Illustration of simplex
Figure 8.2 Simplicial complex
Figure 8.3 Betti numbers
Figure 8.4 Filtration
Figure 8.5 Persistence diagram
Figure 8.6 Schematic representation of TDA
Figure 8.7 Application of TDA

Chapter 9: Bayesian Analysis

Figure 9.1 ABC steps
Figure 9.2
Figure 9.3 ABC steps cont'd
Figure 9.4 ABC step 1
Figure 9.5 ABC step 2
Figure 9.6 ABC step 3
Figure 9.7 ABC step 4
Figure 9.8 ABC step 5
Figure 9.9 Trace. (a) Intercept, (b) degradation rate, (c) white noise
Figure 9.10 Kernel density. (a) Intercept, (b) degradation rate, (c) white noise
Figure 9.11 Autocorrelation plot. (a) Intercept, (b) degradation rate, (c) white noise
Figure 9.12 Example of ABC simulations (histograms)

Chapter 10: Basic Bayesian Nonparametrics

Figure 10.1 Stick-breaking process
Figure 10.2 Chinese restaurant process
Figure 10.3 Chinese restaurant process continued

Chapter 11: Basic Metaheuristics

Figure 11.1 Relationship between data science with evolutionary algorithms and swarm intelligence (Cheng et al., 2016) Reproduced with the permission of BioMed Central Ltd

Chapter 12: Differential Privacy

Figure 12.1 Sensitivity function
Figure 12.2 General structure of differential privacy
Figure 12.3 An example of DP in rail tank safety

List of Tables

Chapter 1: Introduction

Table 1.1 Taxonomy of big data in railway engineering
Table 1.2 Engineering problems
Table 1.3 Track inspection technologies.
Table 1.4 Vertical track forces
Table 1.5 Indicators for each type of defect according to EN 13848-5 (Teixeira and Andrade, 2014) Reproduced with the permission of Springer
Table 1.6 Summary of literature review^a).
Table 1.7 Rail defects classification
Table 1.8 Transverse defects
Table 1.9 Longitudinal defects
Table 1.10 Web defects
Table 1.11 Base defects
Table 1.12
Table 1.13 Surface defectsWheel burns
Table 1.14 NDT techniques for the rail industry.
Table 1.15 Automated visual railway component inspection methods
Table 1.16 Big data versus traditional data

Chapter 2: Data Analysis – Basic Overview

Table 2.1 Examples of symbolic variables

Chapter 3: Machine Learning: A Basic Overview

Table 3.1 Confusion matrix
Table 3.2 Sample of deep learning application in railway track engineering
Table 3.3 Dominant rail group structural distresses
Table 3.4 Dominant sleeper, fastening, and ballast structural distresses
Table 3.5 Definition of track classes
Table 3.6 Maintenance and repair strategies
Table 3.7 Decision table
Table 3.8 Consistent table
Table 3.9 Reduced set of independent variables of decision rules
Table 3.10 Equations to determine numerical parameters of the LogLog Counter
Table 3.11 Dependency between the sketch size and accuracy
Table 3.12 Streaming techniques
Table 3.13 Application of machine learning techniques.

Chapter 4: Basic Foundations of Big Data

Table 4.1 System for large data applications
Table 4.2 Comparison between big data and traditional data
Table 4.3 Traditional data warehousing versus big data issues
Table 4.4 Comparison between stream processing and batch processing
Table 4.5 Taxonomy of big data methods in railway track engineering
Table 4.6 Key definitions of railway track engineering
Table 4.7 Data definition
Table 4.8 Railway track engineering and big data

Chapter 5: Hilbert–Huang Transform, Profile, Signal, and Image Analysis

Table 5.1 Classification of track vertical defects upon their wavelengths
Table 5.2 Comparison between Fourier, wavelet, and HHT
Table 5.3 Some applications of HHT in railway track engineering analysis

Chapter 7: Copula Models

Table 7.1 Archimedean copulas
Table 7.2 Kendall and Spearman's values
Table 7.3 Correlation matrix based on Kendall's tau
Table 7.4 The empirical Kendall's $c07-math-289$ matrix and the sum over the absolute entries of each row for the track geometry data set
Table 7.5 The empirical Kendall's $c07-math-307$ matrix and the sum over the absolute entries of each row for the derailment data set given alignment (right) ( $c07-math-308$ ) as first root
Table 7.6 Properties of pair-copula families considered
Table 7.7 Log-likelihood, number of parameters, AIC, and BIC for $c07-math-340$ -vine and $c07-math-341$ -vine copula models using maximum likelihood estimation (MLE) or sequential estimates

Chapter 8: Topological Data Analysis

Table 8.1 Equivalent definitions of the cycle and boundary groups

Chapter 9: Bayesian Analysis

Table 9.1 Conjugate prior distributions
Table 9.2 Cross-level data^a
Table 9.3 Selected case studies of Bayesian analysis in railway track engineering

Chapter 11: Basic Metaheuristics

Table 11.1 Selected examples

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Title: Big data and differential privacy : analysis strategies for railway track engineering / Nii O. Attoh-Okine.

Description: Hoboken, NJ : John Wiley & Sons, 2017. | Series: Wiley series in operations research and management science | Includes bibliographical references and index.

Identifiers: LCCN 2017005398 (print) | LCCN 2017010092 (ebook) | ISBN 9781119229049 (cloth) | ISBN 9781119229056 (pdf) | ISBN 9781119229063 (epub)

Subjects: LCSH: Railroad tracks\endash Mathematical models. | Data protection-Mathematics. | Big data. | Differential equations.

Classification: LCC TF241 .A88 2017 (print) | LCC TF241 (ebook) | DDC 625.1/4028557-dc23

Preface

The ability of railway track engineers to handle and process large and continuous streams of data will provide a considerable opportunity for railway agencies. This will help decision makers to make informed decisions about the maintenance, reliability, and safety of the railway tracks. Now a period is beginning in which the problem is collecting the railway track data and analyzing it in a defined period of time. Therefore, the tools and methods needed to achieve this analysis need to be addressed. Knowledge derived from big data analytics in railway track engineering will become one of the foundational elements of any railway organization and agency. Also, another key issue has been the protection of data by different railway organizations. Therefore, although the data are available, they are really shared among different agencies. This makes the issue of differential privacy of utmost importance in the railway industry. Also, it is not clear if the industry has developed a clear way of both protecting and accessing the data from third parties.

Data science is an emerging field that has all the characteristics needed by railway track engineers to address and handle the enormous amounts of data generated by various technology platforms currently in place. The major objective is for railway track engineers to have an understanding of big data. Using the right tools and methodologies, railway track big data will also uncover new directions for monitoring and collecting railway track data; this apart from the engineering side will also have a major business impact on railway agencies.

This book provides the fundamental concepts needed to work with big data applications for railway engineers. The concepts serve as a foundation, and it is assumed that the reader has some understanding of railway engineering. The book does not attempt to address railway track engineering as a subject, but it does address the use of data science and the big data paradigm in railway track applications. Colleagues in industry will find the book very handy, but it will also serve as a new direction for graduate students interested in data science and the big data paradigm in infrastructure systems. The work in this book is intended to be accessible to an audience broader than those in railway track engineering.

Furthermore, I hope to shed a bright light on the enormous potential and future development that the big data paradigm will bring to railway track engineering. Theamount of data railway agencies already have and the amount they are planning to collect in the future make this book an important milestone. This book attempts to bring together new emerging topics in a coherent way that can address different methodologies that can be used in solving a variety of railway track problems in the analysis of large data from various inspection technologies. In preparing the book, I tried to achieve the following objectives: (a) to develop some data science ontologies, (b) to provide the formulation of large railway track data using big data analytics, (c) to provide direction on how to present the data (visualization of the results), (d) to provide practical applications for the railway and infrastructure industry, and (e) to provide a new direction in railway track data analysis.

Finally, I assume full responsibility for any errors in the book. The opinions presented in the book represent my experiences in civil infrastructure systems, machine learning, signal analysis, and probability analysis.

January, 2016

Nii O. Attoh-Okine
Newark, Delaware, USA

Acknowledgments

I would like to thank the staff of John Wiley & Sons, Inc., especially Susanne Steitz-Filler, for their time. I would also like to thank Dr. Allan Zarembski and Joe Palese and Hugh Thompson of FRA for their support and encouragement. Thanks also to my current and former graduate students Dr. Yaw Adu-Gyamfi, Dr. Offei Adarkwa, and Emmanuel Martey for offering constructive criticisms. Special thanks to Silvia Galvan-Nunez who additionally provided me support with the complex LaTex issues. I would also like to thank Erin Huston for editing the first draft of the book. Finally, as always, I would like to thank my family: my two children, Nii Attoh and Naa Djama; my wife, Rebecca, for providing the peace and excellent working environment; and my brother, Ashalley Attoh-Okine, an excellent actuary and energy expert, who introduced me to so many data analysis techniques, which have been part of my research over the years. I dedicate the book to the memory of my parents, Madam Charkor Quaynor and Richard Ayi Attoh-Okine, and my maternal grandparents, Madam Botor Clottey and Robert Quaynor.

Big Data and Differential Privacy

Analysis Strategies for Railway Track Engineering

Preface

Acknowledgments